IrMO 2021 Problem 3

For each integer $n \ge 100$ we define $T(n)$ to be the number obtained from $n$ by moving the two leading digits to the end. For example, $T(12345) = 34512$ and $T(100) = 10$ . Find all integers $n \ge 100$ for which $n + T(n) = 10n$ .